{"id":15055,"date":"2025-07-25T09:18:02","date_gmt":"2025-07-25T14:18:02","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=15055"},"modified":"2025-07-30T10:19:29","modified_gmt":"2025-07-30T15:19:29","slug":"phd-dissertation-defense-mr-joe-paulson","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/phd-dissertation-defense-mr-joe-paulson\/","title":{"rendered":"PhD Dissertation Defense: Mr. Joe Paulson"},"content":{"rendered":"

\"\"<\/h1>\n

Theory of Z_n – Structures<\/h1>\n

Mr. Joe Paulson
\nGraduate Student<\/em>
\nUniversity of Wisconsin-Milwaukee<\/p>\n

In this defense, we discuss the boundaries of Type F_n groups; those being groups whose K(G,1) complex has a finite n-skeleton. The boundaries we develop extend the notion of Z-boundaries to what we call Z_n-boundaries. This extension centers around groups no longer acting geometrically on contractible spaces, but instead n-connected spaces. Immediately this means the major theorems of “Boundary Swapping” and “Shape Equivalence of Z-Boundaries” will need revision, but a more subtle point to be discussed is that the category of spaces must also be generalized.<\/p>\n

After discussing the foundation work for a theory of Z_n-boundaries, we end with an exploration how these new structures can be related to other well-known compactifications such as the one-point compactification, end-point compactification, and Z-compactifications.<\/p>\n

Advisor:
\nCraig Guilbault<\/p>\n

Committee Members:
\nBoris Okun, Chris Hruska, Jonah Gaster, and Pamela Harris<\/p>\n","protected":false},"excerpt":{"rendered":"

Theory of Z_n – Structures Mr. Joe Paulson Graduate Student University of Wisconsin-Milwaukee In this defense, we discuss the boundaries of Type F_n groups; those being groups whose K(G,1) complex has a finite n-skeleton. 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